From 1987-88 to 1990-91 the Cornwall, Ontario native was a mainstay on the Red Raiders blue line leading them to the 1990 NCAA Championship game against Wisconsin, a game that they lost 7-3. In 1991-92 Poapst signed as a free agent with the ECHL's Hampton Road Admirals, a team with whom he spent two seasons with capturing the 1992 Riley Cup and earning ECHL First Team All-Star honors in 1993.

While Poapst spent the majority of the 1992-93 season in Hampton Roads, he also played a handful of games with the AHL's Baltimore Skipjacks. Following his First Team All-Star honors in 1993, Poapst joined the AHL's Portland Pirates in 1993-94 and spent the next seven seasons with the team.

After two strong seasons in Portland, the Washington Capitals signed Poapst as a free agent midway through the 1994-95 season. Although he spent the majority of the 1995-96 season with Portland leading them to the 1996 Calder Cup finals only to lose against the Rochester Americans, Poapst did make his NHL debut playing in three games with the Capitals, scoring his first NHL goal before returning to Portland the following season.

Poapst returned to Washington's line up in 1998-99 where he played in a season high 22 games with the Capitals before signing as a free agent with the Chicago Blackhawks in the summer of 2000. In his first season with the Blackhawk organization, Poapst split his season with Chicago and their AHL affiliate in Norfolk before returning to the Blackhawk line up in 2001-02.

After a strong season in 2001-02, Poapst enjoyed his most productive season offensively to date in 2002-03 when he notched 13 points (2-11-13) and was a +14 on a struggling Hawks team. The Cornwall native went on to play one more season with Chicago before having his rights acquired by the Pittsburgh Penguins prior to the 2005-06 season. Poapst went on to play 21 games for the Pens before being dealt to the St. Louis Blues for Eric Boguniecki.